Global well-posedness for 2D generalized parabolic Anderson model via paracontrolled calculus

This article revisits the problem of global well-posedness for the generalized parabolic Anderson model on R+×T2 within the framework of paracontrolled calculus (Gubinelli et al. in Forum Math, 2015). The model is given by the equation: (Formula presented.) where η∈C-1-κ with 1/6>κ>0, and F∈Cb2(R). Assume that η∈C-1-κ and can be lifted to enhanced noise, we derive new a priori bounds. The key idea follows from the recent work by Chandra et al. (A priori bounds for 2-d generalised Parabolic Anderson Model,, 2024), to represent the leading error term as a transport type term, and our techniques encompass the paracontrolled calculus, the maximum principle, and the localization approach (i.e. high-low frequency argument).